<p>Linguistics needs to embrace all the way down a key feature of language: its diversity. In this paper, we build on recent experimental findings and theoretical discussions about the neuroscience and the cognitive science of linguistic variation, but also on proposals by theoretical biology, to advance some future directions for a more solid neurocognitive approach to language diversity. We argue that the cognitive foundations and the neuroscience of human language will be better understood if we pursue a unitary explanation of four key dimensions of linguistic variation: the different functions performed by language, the diversity of sociolinguistic phenomena, the typological differences between human languages, and the diverse developmental paths to language. Succeeding in the cognitive and neurobiological examination and explanation of these four dimensions will not only result in a more comprehensive understanding of how our brain processes language, but also of how language evolved and the core properties of human language(s).</p>